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arXiv:cond-mat/0602033 · Physical Review B

Two-dimensional Heisenberg antiferromagnet in a transverse field

Peter J. Jensen, Karl H. Bennemann, Dirk K. Morr, Hugues Dreyssé

Published Apr 6, 2006• 20 citations
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Abstract

We investigate the magnetic reorientation in a two-dimensional anisotropic antiferromagnet due to a transverse magnetic field. Using a many-body Green's function approach, we show that the magnetization component perpendicular to the applied field (and along the easy axis of the antiferromagnet) initially increases with increasing field strength. We show that this unexpected result arises from the suppression of quantum and thermal fluctuations in the antiferromagnet. Above the N\'eel temperature, this effect leads to a reappearance of a magnetic moment along the easy axis.

DOI
10.1103/physrevb.73.144405

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We investigate the magnetic reorientation in a two-dimensional anisotropic antiferromagnet due to a transverse magnetic field. Using a many-body Green's function approach, we show that the magnetization component perpendicular to the applied field (and along the easy axis of the antiferromagnet) initially increases with increasing field strength. We show that this unexpected result arises from the suppression of quantum and thermal fluctuations in the antiferromagnet. Above the N'eel temperature, this effect leads to a reappearance of a magnetic moment along the easy axis.
We investigate one-dimensional S=1/2S=1/2S=1/2 and S=1S=1S=1 antiferromagnetic quantum-spin chains with easy-axis anisotropies in a transverse field. We calculate both the uniform magnetization and the staggered magnetization, using a variant of the density-matrix renormalization-group method. We find that the staggered magnetizations exhibit reentrant behavior as functions of the transverse field, where the competition between the classical N\'eel order and the quantum fluctuations plays an important role. We also discuss the critical behavior associated with the staggered magnetizations.
We discuss a pseudospin representation of the two-dimensional $t\text{\ensuremath{-}}J$ model. We introduce pseudospins associated with empty sites, deriving a representation of the $t\text{\ensuremath{-}}J$ model that consists of local spins and spinless fermions. We show, within a mean-field approximation, that our representation of $t\text{\ensuremath{-}}J$ model corresponds to the isotropic antiferromagnetic Heisenberg model in an effective magnetic field. The strength and the direction of the effective field are determined by the hole doping $\ensuremath{\delta}$ and the orientation of pseudospins associated with empty sites, respectively. We find that the staggered magnetization in the standard representation corresponds to the component of magnetization perpendicular to the effective field in our pseudospin representation. Using a many-body Green's function method, we show that the staggered magnetization decreases with increasing hole doping $\ensuremath{\delta}$ and disappears at $\ensuremath{\delta}\ensuremath{\approx}0.06--0.12$ for t∕J=2.5−−5t∕J=2.5--5t∕J=2.5−−5. Our results are in good agreement with experiments and numerical calculations in contradistinction to usual mean-field methods.
We consider the one-dimensional Ising-like fully anisotropic S = 1/2 Heisenberg antiferromagnetic Hamiltonian and study the dynamics of domain wall excitations in the presence of a transverse magnetic field h x . We obtain dynamical spin correlation functions along the magnetic field, S xx ( q ,ω), and perpendicular to it, S yy ( q ,ω). It is shown that the line shapes of S xx ( q ,ω) and S yy ( q ,ω) are purely symmetric at the zone boundary. It is observed in S yy ( q ,ω) for π/2< q <π that the spectral weight moves toward the low-energy side with the increase of h x . This model is applicable to the study of the spin dynamics of CsCoCl 3 in the presence of weak interchain interactions.
The ground-state properties of the spin-1/2 antiferromagnetic Heisenberg model with spatially anisotropic couplings on a square lattice are investigated by a spin-rotation-invariant Green's-function approach and by Lanczos diagonalizations on lattices up to 36 sites supplemented by finite-size scaling. We focus on the anisotropy-driven transition from the N\'eel state to a paramagnetic state with antiferromagnetic short-range order and on the spatial dependence of spin correlation functions. Our principal result is that a rather sharp crossover in the magnetic behavior occurs at the coupling ratio ${R}_{0}\ensuremath{\simeq}0.2 {(R=J}_{y}{/J}_{x}).$
Low dimensionality enhances quantum fluctuations, triggering novel states of quantum matter to emerge. In real materials, low dimensionality usually arises from spatially strongly anisotropic couplings. Here, we demonstrate a different mechanism: in two-dimensional systems with coupled alternating ferromagnetic (FM) and antiferromagnetic (AFM) spin-1/21/21/2 chains, an applied magnetic field may drive a dimensional reduction. Under magnetic field, the FM chains polarize and stiffen, suppressing the propagation of transverse AFM fluctuations from one chain to another, and effectively induce one-dimensional behavior at low energies. For a model describing botallackite, Cu2_22​(OH)3_33​Br, quantum Monte Carlo dynamics show that beyond a critical magnetic field, the low-energy spectrum reduces to that of a one-dimensional AFM Heisenberg spin-1/21/21/2 chain with field-dependent incommensurate two-spinon fluctuations, providing clear signatures for inelastic neutron scattering.
The effect of the transverse magnetic field h x on the spin dynamics of a one dimensional Ising-like S =1/2 antiferromagnet is discussed. Based on a picture of the propagating domain walls, we obtain dynamical spin correlation functions along the magnetic field S x x ( k ,ω) and perpendicular to it S y y ( k ,ω). A remarkable effect is seen in S y y ( k ,ω) for π/2 ≤ k ≤π, where the spectral weight moves toward the low energy side with the increase of h x . The theory is applied to the analysis of the spin dynamics of CsCoCl 3 , taking into account weak interchain interactions. Zeeman ladders occur and S y y ( k , ω) for k ∼π exhibits a novel feature under the existence of h x .